Curiosities: History of linear algebra
Its ideas have been around for a long time
Although linear algebra is regarded as a relatively modern mathematics topic, its ideas have been around for a long time.
The first instance of the solution of a system of linear equations, using what is nowadays called Gaussian elimination, can be found in the eighth chapter of the text Nine Chapters on the Mathematical Art, written by Chinese scholars around 3,000 years ago. In stark contrast, Gaussian elimination was introduced to the western world by Sir Isaac Newton in 1669.
The theory of determinants was, likewise, introduced to humankind by the eastern world prior to the western one. This time, Japan takes the honours; Seki Takakazu, known as the ‘Japanese Newton’, is credited to be the first who described determinants in 1683, a few years before Gottfried Wilhelm Leibniz’s first work on the subject.
Perhaps surprisingly, matrices were envisioned after determinants. It was James Joseph Sylvester who coined the word ‘matrix’ – meaning ‘womb’ – in 1848. A few years earlier, Hermann Grassmann, considered the father of modern linear algebra, conceived what nowadays we call vector spaces and linear independence.
At around the same time, Sir William Rowan Hamilton invented the quaternions, and with them, the terms ‘vector’ – from the Latin word vehere, meaning ‘to carry’ – and ‘scalar’, used to scale vectors.
Later, in 1856, Arthur Cayley, who collaborated a lot with Sylvester, introduced matrix multiplication and matrix inversion, in the process linking matrices with determinants.
